Vectors in the Plane

Disclaimer: The material in the videos below comes mainly from outside City Tech. The presentation in these videos may differ from the one given in your class. Please consult with your instructor to confirm whether a particular approach is acceptable in your class.

1. $\rhd$ Introduction to vectors and scalars (8:38) A discussion on vectors and scalars.
2. $\rhd$ Recognizing vectors (2:35) Which of the following can represent a vector? Select all that apply.
   1. The number 5
   2. The angle measure $5^{\circ}$
   3. The point $(5,5)$
   4. The outcome of $5+5$
3. * Practice: Recognizing vectors. (2 problems)
4. $\rhd$ Equivalent vectors (6:36) When are two vectors equivalent.
5. * Practice: Equivalent vectors. (4 problems)
6. $\rhd$ Finding the magnitude (3:05) The magnitude of $\vec{a}= \langle 5,-3\rangle$.
7. $\rhd$ Scalar multiplication of vectors (5:41) Given that $\vec{w}= \langle 1,2\rangle$, find $3\vec{w}$ and $-2\vec{w}$. What do they represent geometrically?
8. * Practice: Scalar multiplication. (4 problems)
9. $\rhd$ Adding and subtracting vectors (7:41) Given that $\vec{a}= \langle 3,-1\rangle$ and $\vec{b}= \langle 2,3\rangle$, what are $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$?  What do they represent geometrically?
10. $\rhd$ Combined vector operations (5:58) Given that $\vec{u}= \langle 2,-1\rangle$ and $\vec{w}= \langle -5,5\rangle$, what are $3\vec{u}+\dfrac{1}{5}\vec{w}$ and $\vec{a}-\vec{b}$? What does it represent geometrically?
11. * Practice: Combined vector operations. (4 problems)
12. $\rhd$ Finding unit vector with given direction (5:01) Find a unit vector in the direction of $\vec{a}= \langle 3,4\rangle$.
13. * Practice: Unit vectors. (4 problems)
14. $\rhd$ Direction of a vector (1st and 2nd quadrant) (9:00) Find the directions of $\vec{u}= \langle 3,4\rangle$ and $\vec{w}= \langle -5,6\rangle$.
15. $\rhd$ Direction of a vector (3rd and 4th quadrant) (6:41) Find the directions of $\vec{a}= \langle -2,-4\rangle$ and $\vec{b}= \langle 4,-6\rangle$.
16. * Practice: Direction of vectors. (4 problems)
17. $\rhd$ Find magnitude and angle of a vector (5:09) Find magnitude and angle of $\langle 2, -2\sqrt{3}\rangle$